1. Field of the Invention
The invention relates to a packet transmission system comprising at least a terminal and a head station, the head station comprising means for receiving packets of data transmitted by said terminal with a frequency error xcex94f, and error estimation means for computing, on the basis of the received data, a discrete error function Z(xcex94{circumflex over (f)}) and for deriving an estimation xcex94{circumflex over (f)} of the frequency error corresponding to a maximum value of the error function Z(xcex94{circumflex over (f)}) for a given accuracy (Acc).
The invention also relates to a receiver for a packet transmission system intended to receive packets of data transmitted by a terminal with a frequency error xcex94f and comprising error estimation means for computing, on the basis of the received data, a discrete error function Z(xcex94{circumflex over (f)}) and for deriving an estimation xcex94{circumflex over (f)} of the frequency error corresponding to a maximum value of the error function Z(xcex94{circumflex over (f)}) for a given accuracy (Acc).
The invention further relates to a method of frequency correction at the receiver end for a packet transmission system, comprising
a step of receiving packets of data from at least one terminal of said system,
an error estimation step for computing, on the basis of the received data, a discrete error function Z(xcex94{circumflex over (f)}) and for deriving a frequency error estimation xcex94{circumflex over (f)} relative to the data received and corresponding to a maximum value of the error function Z(xcex94{circumflex over (f)}) for a given accuracy (Acc).
The invention finds important applications, notably in the field of cable or satellite transmissions with return paths in which a plurality of terminals can transmit data packets to a head station in accordance with a frequency and time division mechanism. Such transmissions from terminals to the head station are referred to as ascending transmissions.
These terminals are generally intended for the consumer. It is thus important to reduce their cost price. To this end, it is advantageous to use low-cost local oscillators which are, however, relatively inaccurate, for generating the carrier frequencies to be used in the ascending transmissions. Typically, the oscillators used have an accuracy varying between 1 ppm (part per million) and 10 ppm. The error resulting in the generated carrier frequency is proportional to the carrier frequency and is larger as the frequencies used are higher. By way of example, in the satellite transmission systems using the frequency band Ka (20 GHz-30 GHz) for the ascending transmissions, the width or frequency error observed for a local oscillator having an accuracy of 1 ppm may reach xc2x130 kHz (i.e. for a symbol frequency of 100 kHz, the standard frequency width with respect to the symbol frequency is xc2x130%).
2. Description of Related Art
The article xe2x80x9cFrequency estimator with dichotomous search of periodogram peakxe2x80x9d by Y. V. Zakharov and T. C. Tozer, published in the magazine Electronics Letters, vol. 35, no. 19, Sep. 16, 1999, describes a frequency estimator which is based on an algorithm named after its authors Rife and Boorstyn for estimating a frequency error in a frequency range which is standardized with respect to the symbol frequency xcex94f/B of xc2x1xc2xd (where xcex94f is the frequency error and B is the symbol frequency). In the description hereinafter, the estimation of the standard frequency width xcex94f/B or xcex94fxc3x97Ts (where Ts is the duration symbol) which is to be determined will be denoted xcex94{circumflex over (f)}. The received data are modulated in accordance with a modulation of the PSK (Phase Shift Keying) type for forming symbols.
The estimators are characterized by different parameters, notably by the accuracy of the obtained estimation which is denoted Acc, the magnitude of the acquisition range of the frequency width denoted xc2x1xcex94fmax, the minimum level with respect to the signal-to-noise ratio of the treated signal, and the complexity of the algorithm. Certain parameters have opposite evolutions. Particularly the accuracy of the estimation is less as the acquisition range is larger; and the estimators are more complex as they are capable of functioning at lower signal-to-noise ratios. Rife and Boorstyn have shown that the frequency error xcex94f has a maximum probability of being situated at the location of the maximum amplitude of the following function, denoted Z(xcex94{circumflex over (f)}):                               Z          ⁡                      (                          Δ              ⁢                              xe2x80x83                            ⁢                              f                ^                                      )                          =                              1            L                    ⁢                                    ∑                              k                =                0                                            L                -                1                                      ⁢                          xe2x80x83                        ⁢                                          z                ⁡                                  (                  k                  )                                            xc3x97                              ⅇ                                                      -                    j2                                    ⁢                                      xe2x80x83                                    ⁢                  nk                  ⁢                                      xe2x80x83                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                                      f                    ^                                                                                                          (        1        )            
wherein L is the length of observation, i.e. the number of received symbols used for computing the error estimation, and k represents the position of the symbol in the received frame, with z(k)=x(k)xc3x97ck* if the received symbols are known, where ck* is the conjugated complex of the known predetermined symbol ck and where x(k) is the symbol received with a frequency error xcex94f and is written as x(k)=ckxc3x97e2xcfx80j.kxcex94fxc3x97TS+jxcfx860 where xcfx860 is the inititial phase shift between the local oscillator used at the receiver end and that used at the transmitter end (this phase shift is different for each packet and corresponds to the phase shift for k=0) and with z(k)=ejM arg|x(k)| if the received symbols are not known in advance, where M is the number of PSK modulation phases used but in which case the result obtained must be divided by M so as to obtain the estimation xcex94{circumflex over (f)}.
The technique proposed in the cited article recommends an error estimation in two steps, a first step in which a first error estimation is obtained by computing a Fast Fourier Transform (FFT) for a certain number of points in each standard interval xc2x1xc2xd, and a second step in which successive iterations of error computations are performed for searching the maximum value of the error function in accordance with a dichotomous method by starting from three adjacent points roughly representing of the maximum location. This technique implies that the points are computed in all intervals of acquisition of the standard frequency width xc2x1xc2xd for obtaining the first estimation. In the case of an estimation only using a preamble of predefined data in each received packet for effecting the estimation, currently referred to as DA (Data Aided), the time of acquisition of the error is very limited. It is also preferable to limit the computing power required at the level of the network head by limiting the number of computations. However, this method does not allow adaptation of the number of computations to the real performance of the local oscillators used in the terminals.
It is an object of the invention to remedy these drawbacks by proposing a system, a receiver and a frequency correction method with which the reception of data packets having a large frequency shift can be improved by limiting the number of computations to a maximum by taking the real performance of the terminals used in the system into account. To this end, a transmission system and a receiver according to the invention as described in the opening paragraph are characterized in that the error correction means comprise iteration means for effecting a first iteration of the computation of the error function Z(xcex94{circumflex over (f)}) for 2N+1 error values comprised in a fixed standard range xc2x1xcex94fmax dependent on said terminal for deriving a first frequency error estimation (xcex94{circumflex over (f)}(i)), and successive iterations for values comprised between the current estimation previously calculated, and a neighboring value for which the error function Z(xcex94{circumflex over (f)}) has the largest amplitude, until a predetermined number of iterations (it) related to the accuracy (Acc) is obtained by means of the relation (2):                     Acc        =                              Δ            ⁢                          xe2x80x83                        ⁢                          f              max                                            N            xc3x97                          2                              It                -                1                                                                        (        2        )            
The terminals which are currently on the market and are used in the interactive transmission systems generally have a frequency error comprised in a maximum error range denoted xc2x1xcex94f0/B (where B is the symbol frequency) comprised in the interval xc2x1xc2xd. By computing the function Z(xcex94{circumflex over (f)}) in an error range xc2x1xcex94fmax/B, with xc2xd greater than xcex94fmax/B greater than xcex94f0/B, the invention prevents computation of all the points comprised in the intervals [xe2x88x92xc2xd; xe2x88x92xcex94fmax/B] and [xcex94fmax/B; xc2xd] which are remote from the real error. The invention recommends a first iteration of the function Z(xcex94{circumflex over (f)}) for 2N+1 points comprised in the range xc2x1xcex94fmax/B, where N is an integer chosen in such a way that xcex94fmax/N is of the same order of magnitude as the accuracy obtained with the Rife and Boorstyn algorithm. This first iteration provides a first estimation xcex94{circumflex over (f)}(i) of the searched frequency error. Successive iterations are subsequently performed by computing a single supplementary point at each iteration for a new error value comprised between the previously computed current estimation xcex94{circumflex over (f)}(i), where i is a strictly positive iteration index, and that of two neighboring values already computed, for which the function Z(xcex94{circumflex over (f)}) has the largest amplitude. The result is subsequently compared with the current estimation xcex94{circumflex over (f)}(i) for deriving a new estimation which is equal to the maximum value between the current estimation xcex94{circumflex over (f)}(i) and the new result. The computation is thus re-iterated until the number of predetermined iterations it in accordance with equation (2) has been obtained.
In accordance with a characteristic feature of the invention, for every new packet received from a given terminal, the range xc2x1xcex94fmax is fixed as a function of the error estimation xcex94{circumflex over (f)} obtained for the previous packets. This measure allows a reduction or an extension of the search interval of the frequency error as a function of the real performance of the local oscillator used in each terminal.
Similarly, according to the invention, a method of frequency correction at the receiver end is characterized in that the error estimation step comprises the following sub-steps:
a first iteration it, of the error function Z(xcex94{circumflex over (f)}) for 2N+1 error values comprised in a fixed range xc2x1xcex94fmax dependent on said terminal for deriving a first frequency error estimation xcex94{circumflex over (f)}1),
successive iterations (iti+1, with i being a strictly positive iteration index), for values comprised between the current estimation (xcex94{circumflex over (f)}(i)) and a neighboring value for which the error function Z(xcex94{circumflex over (f)}) has the largest amplitude,
a step of comparing the result of each iteration (iti+1) with the current estimation (xcex94{circumflex over (f)}(i)) and for deriving a new estimation (xcex94{circumflex over (f)}i+1)) until a predetermined number of iterations (it) related to the accuracy (Acc) is obtained as defined by the relation (2).
In accordance with a preferred embodiment of the invention, suitable for the DA systems, in which the transmitted data packets comprise a preamble of known data (ck), the system and the receiver are characterized in that the error estimation means comprise means for extracting data from the preamble and in that the error function Z(xcex94{circumflex over (f)}) is computed on the basis of these data extracted from the preamble. The use of known symbols of the preamble for estimating the frequency error at the receiver end is particularly advantageous because it renders the computation of the error function Z(xcex94{circumflex over (f)}) independent of the type of modulation used. The phase of the received symbols x(k)=ckxc3x97e2xcfx80j.kxcex94f+xcfx860 of the module |ck| contained in the preamble comprises information on the real error xcex94f. By multiplying the symbol of the received preamble x(k) by the conjugated complex of the corresponding known symbol ck*, one obtains the information of the phase containing the information of the searched frequency error.
These and other aspects of the invention are apparent from and will be elucidated, by way of non-limitative example, with reference to the embodiments described hereinafter.